The prior art may be disclosed in some of the following publications. In the specification a prior art reference will be addresses by referring to the number of that prior art reference in the list. For example the first prior art reference in the list will be referred to as [1]:                1. A. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Transactions on Information Theory, 29, 543-551 (1983).        2. E. Ip and J. M. Kahn, “Carrier synchronization for 3- and 4-bit-per-Symbol optical transmission,” J. Lightwave Technol., 23, 4110-4124 (2005).        3. R. Noé, “PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I & Q baseband processing,” Photon. Technol. Lett., 17, 2004-2006 (2005).        4. M. G. Taylor, “Accurate digital phase estimation process for coherent detection using a parallel digital processor,” in, ECOC'05 European Conf. of Optical Communication, Tu 4.2.6 (2005).        5. E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol., 25, 2675-2692 (2007).        6. S. Hoffmann et al., “Frequency and phase estimation for coherent QPSK transmission with unlocked DFB lasers,” Photon. Technol. Lett., 20, 2008-2010 (2008).        7. M. G. Taylor, “Detection using digital signal processing,” J. Lightwave Technol., 27, 901-914 (2009).        8. M. G. Taylor, “Algorithms for coherent detection What can we learn from other fields?,” in OFC/NFOEC'10, Conf. on Optical Fiber Communication, OThL4 (2010).        9. M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol., 27, 901-914 (2009).        10. K. Piyawanno, M. Kuschnerov, B. Spinnler, and B. Lankl, “Low complexity carrier recovery for coherent QAM using superscalar parallelization,” in ECOC'10 European Conf. of Optical Communication, We.7.A.3 (2010)        11. D. Divsalar and M. K. Simon, “Multiple-symbol differential detection of MPSK,” IEEE Trans. Comm., 38, 300-308 (1990).        12. F. Edbauer, “Bit error rate of binary and quaternary DPSK signals with multiple differential feedback detection,” IEEE Trans. Comm., 40, 457-460 (1992).        13. M. Adachi and F. Sawahashi, “Decision feedback multiple-symbol differential detection for M-ary DPSK,” Electron. Lett., 29, 1385-1387 (1993).        14. F. Adachi and M. Sawahashi, “Decision feedback differential phase detection of M-ary DPSK signals,” IEEE Trans. Vehicular Technol., 44, 203-210 (1995).        15. S. Zhang, P. Y. Kam, J. Chen, and C. Yu, “Decision-aided maximum likelihood detection in coherent optical phase-shift-keying system,” Optics Express, 17, 703-715 (2009).        16. C. Yu, S. Zhang, P. Y. Kam, and J. Chen, “Bit-error rate performance of coherent optical M-ary PSK/QAM using decision-aided maximum likelihood phase estimation,” Optics Express, 18, 12088-103 (2010).        17. S. Zhang, P.-yuen Kam, C. Yu, and J. Chen, “Decision-aided carrier phase estimation for coherent optical communications,” J. Lightwave Technol., 28, 1597-1607 (2010).        18. D. van den Borne, S. Calabro, S. L. Jansen, E. Gottwald, G. D. Khoe, and H. de Waardt, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” in OFC'05 Conference on Optical Fiber Communication (2005).        19. M. Nazarathy and Y. Yadin, “Approaching coherent homodyne performance with direct detection low-complexity advanced modulation formats,” in COTA'06 Coherent Optical Technologies and Applications (2006).        20. X. Liu, “Data-Aided Multi-Symbol Phase Estimation for Receiver Sensitivity Enhancement in Optical DQPSK, CThB4,” in COTA'06 Coherent Optical Techniques and Applications (2006).        21. M. Nazarathy and Y. Atzmon, “Approaching coherent homodyne performance with direct detection low-complexity advanced modulation formats,” in COTA'08 Coherent Optical Techniques and Applications (2008).        22. X. Liu, S. Chandrasekhar, and A. Leven, “Digital self-coherent detection,” Optics Express, 16, 792-803 (2008).        23. M. Nazarathy, X. Liu, L. Christen, Y. K. Lize, and A. E. Willner, “Self-Coherent Multisymbol Detection of Optical Differential Phase-Shift Keying,” J. Lightwave Technol., 26, 1921-1934 (2008).        24. Y. Takushima, H. Y. Choi, and Y. C. Chung, “Transmission of 108-Gb/s PDM 16ADPSK signal on 25-GHz grid using non-coherent receivers,” Optics Express, 17, 13458-66 (2009).        25. J. Li et al., “Self-coherent receiver for PoIMUX coherent signals,” in OFC'11 Conf. on Optical Fiber Communication, OWV5 (2011).        26. N. Kikuchi and S. Sasaki, “Highly sensitive optical multilevel transmission of arbitrary quadrature-amplitude modulation (QAM) signals with direct detection,” J. Lightwave Technol., 28, 123-130 (2010).        27. N. Kikuchi, “Chromatic dispersion-tolerant higher-order multilevel transmission with optical delay detection,” in SPPCom'11 Signal Processing in Photonic Communications—OSA Technical Digest (2011).        28. S. Adhikari et al., “Self-coherent optical OFDM: an interesting alternative to direct or coherent detection” in ICTON'11 13th International Conference on Transparent Optical Networks (2011).        29. S. Kumar, Impact of Nonlinearities on Fiber Optic Communications, (Springer, 2011).        30. N. Sigron, I. Tselniker, M. Nazarathy, A. Gorshtein, D. Sadot, and I. Zelniker, “Ultimate single-carrier recovery for coherent detection,” in OFC'11 Conference on Optical Fiber Communication, OMJ2 (2011).        31. M. Nazarathy, N. Sigron, and I. Tselniker, “Integrated carrier phase and frequency estimation for coherent detection based on multi-symbol differential detection (MSDD),” in SPPCom'11 Signal Processing in Photonic Communications—OSA Technical Digest, Invited paper SPMC1 (2011).        32. N. Kikuchi, S. Sasaki, and T. Uda, “Phase-noise tolerant coherent polarization-multiplexed 16 QAM Transmission with digital delay-detection, in ECOC'11 European Conference of Optical Communication (ECOC), Tu.3.A (2011).        33. T. Adali and S. Haykin, Adaptive signal processing—next generation solutions, (John Wiley, 2010).        34. W. Shieh and K.-po Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Optics Express, 16, 15718-15727 (2008).        35. Y. Atzmon and M. Nazarathy, “A gaussian polar model for error rates of differential phase detection impaired by linear, nonlinear, and laser phase noises,” J. Lightwave Technol., 27, 4650-4659 (2009).        